Obesity is associated with diseases such as diabetes and heart disease and with decreased longevity. This might suggest that, among obese individuals, weight loss will increase longevity, but this has yet to be demonstrated. Most epidemiologic studies find that weight loss predicts decreased longevity. However, an emerging body of research suggests that, when analyses are confined to obese individuals who profess an intention to lose weight, subsequent weight loss is associated with no harmful effect and perhaps a very modest decrease in mortality rate. We hypothesize that this very modest (at best) beneficial association of weight loss with reduced mortality rate among people who intend to lose weight results from the fact that, even among people who intend to lose weight, subsequent weight change is a mixture of intentional weight loss (IWL) and unintentional weight loss (UWL). The UWL may have opposing effects to IWL, thereby canceling out beneficial effects of IWL that may exist. Unfortunately, for any individual, we cannot directly observe how much of their weight change was due to their intention and how much was due to factors beyond their intention. This makes it impossible to directly estimate effects of IWL in epidemiologic studies or, for that matter, in randomized clinical trials and even animal studies of caloric restriction and aging. We have developed a novel statistical method that can place plausible boundaries around the effects of IWL on mortality rate (or any other measurable outcome). Preliminary studies suggest that the actual effect of IWL on mortality rate may be strongly beneficial. Here, we propose to expand our method from its current incarnation in ordinary least squares to allow for censured survival times to facilitate application to a broader range of circumstances. Moreover, we propose expanding the method to allow for calculation of confidence intervals and standard errors, allowing for non-linearity in relationships, tightening the plausible boundaries of estimated effects, rigorously evaluating the properties of the method by simulation studies, and applying the methods to data from a longevity study of experimental organisms and a human epidemiologic study. Our proposed research not only has value in and of itself, but can add value to many studies of weight loss in humans and caloric restriction in experimental models, thereby increasing the value of NIH's substantial ongoing investment in such studies.